On the Decompositions of Intervals and Simple Closed Curves

Adam Grabowski

University of Bialystok

Summary.

The aim of the paper is to show that the only subcontinua of the Jordan curve are arcs, the whole curve, and singletons of its points. Additionally, it has been shown that the only subcontinua of the unit interval $\Bbb I$ are closed intervals.

This work has been partially supported by the European Community TYPES grant IST-1999-29001 and CALCULEMUS grant HPRN-CT-2000-00102.

MML Identifier: BORSUK_4

Contents (PDF format)

1. Preliminaries
2. Decompositions of Intervals
3. Decompositions of Simple Closed Curves

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